Abstract
STU supergravity becomes an integrable system for solutions that effectively only depend on two variables. This class of solutions includes the Kerr solution and its charged generalizations that have been studied in the literature. We here present an inverse scattering method that allows to systematically construct solutions of this integrable system. The method is similar to the one of Belinski and Zakharov for pure gravity but uses a different linear system due to Breitenlohner and Maison and here requires some technical modifications. We illustrate this method by constructing a four-charge rotating solution from flat space. A generalization to other set-ups is also discussed.
Highlights
The class of models considered typically involves a finite-dimensional symmetry group G that acts as a solution generating group on the three-dimensional reduced system
Breitenlohner and Maison (BM) have constructed a linear system that is different from that of Belinski and Zakharov (BZ) and that takes the structure of G into account [12]
G = SO(4, 4) is the symmetry that is relevant for the STU model that has multiple constructions from string theory and whose solutions have attracted a lot of attention over the years [15,16,17,18,19]
Summary
We assume that there is a three-dimensional gravity-matter system that has a global symmetry group G and a local symmetry group K that is maximal subgroup of G. The elements k ∈ K satisfy k#k = 1, where the ‘hash’ denotes some generalized anti-involution. For G = SL(n, R) and K = SO(n) this operation is just the usual transposition k# = kT but it can be different in general. With a global g ∈ G and a local gauge transformation k(x) ∈ K. That is independent of the choice of gauge
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